Less than detection limit data

Power calculations for the example data are performed on the untransformed

data. From Equation L-11, the minimum significant difference (dmin , when t1- =

0) for the parametric LSD test is:

d min = ( t 1-α ,v ) 2MSE/n

(L-22)

UCL = 0.190 + 1.746 (0.003763/5)1/2 = 0.238 g/g, where v = 16 df. SAS

conveniently provides this value as the "Least Significant Difference" in the

GLM or ANOVA procedures when the LSD test is requested (and sample sizes

are equal).

The power of the LSD test for detecting a 100 percent increase in dredged

material bioaccumulation over the mean reference bioaccumulation (i.e., d =

0.066 g/g) can be determined by:

t 1-β ,v = d n/2MSE - t 1-α ,v

(L-23)

= (0.066) [5/2(0.003763)]2 - 1.746 = -0.045, and 1 - for t = -0.045 with 16

df is 0.48. Power values for 10, 25, 50, 100, 200 and 300 percent increases over

mean reference bioaccumulation are given in the output for SAS program

BIOACC (Section L.4.2.2).

The sample size (n) required to provide a 0.95 probability (1 - = 0.95) of

detecting a 25 percent increase (0.0165 g/g) over the mean reference

bioaccumulation, calculated using the z-approximation (Eq. 9) with MSE

replacing s2, is:

n = 2(1.645 + 1.645)2[0.003763/(0.0165)2] + 0.25(1.645)2 = 300

(L-24)

Using the same equation, to detect a 100 percent increase (0.066 g/g) over

the mean reference bioaccumulation with a power of 0.95, n = 20. Assuming we

are limited to 5 replicates, there is a 0.95 probability of detecting a difference (d)

of 0.135 g/g, which is a 205 percent increase over the mean reference bioac-

cumulation. Other values of d when power = 0.5, 0.6, 0.7, 0.8, 0.9, and 0.99 are

given in the output for SAS program BIOACC (Section L.4.2.2).

Less than detection limit data. Statistical procedures for bioaccumulation

data analysis in this Appendix cannot be applied directly in the common

situation where some contaminant concentrations are reported only as less than

some numerical detection limit (DL). The actual concentrations of these

"censored" data (hereafter referred to as nondetects) are unknown and are

presumed to fall between zero and the DL. Whenever possible, laboratories that

analyze contaminant residues should be encouraged to report observed

concentrations below DL (Porter, Ward, and Bell 1988), even though the

precision of these measurements is less than that of above DL measurements.

When below-DL concentrations (sometimes called "J-values") are reported, they

should be used as legitimate data in statistical comparisons. On the other hand,

when bioaccumulation samples include nondetects, the unknown values must be

replaced using a censored data method prior to statistical analysis.

L35

Appendix L Selected Resource Documents